Find the x and y coordinates of the points on the curve y 2+xy+x 2 = 4 where the curve has slope − 1 2 .
mathematics
Description
Practice Problems for the Final Exam, Math 16a, Fall 2019
1. Find the x and y coordinates of the points on the curve
y 2+xy+x 2 = 4 where the curve has slope − 1 2 .
2. Use the definition of the derivate as a limit to evaluate the derivative of f(x) = 1/x2 .
3. For each of the following, find the limit value or determine that the limit does not exist.
(a) limx→3 x 3−x 2−6x x2−2x−3
(b) limx→∞ x 2−3x e x
4. Evaluate the first derivatives of the following functions.
(a) f(x) = ln(e √x) e ln(√x) (b) f(x) = x √ x
5. Use the derivative to approximate √
122. Hint: √
121 = 11.
6. Determine the following
